In first quantization, we can read the particle number from the Hamiltonian.
$$
H=\sum_{i=1}^N \hat{T}(x_i)
$$
Converting this to second quantization form, the particle number of the system is lost:
...

I'm trying to figure out how one would write down the hamiltonian of a free fermion system (eventually in second quantization) on a one dimensional lattice and I'm having trouble both coming up with ...

I am studying the quantization of the electromagnetic field. My text quantizes by changing amplitudes to ladder operators, by putting in an action and by imposing bosonic commutation relations upon ...

Imagine we have a N-particle Hamiltonian without any interaction between the electron particles
$$ H = \sum_{i=1}^{N} \frac{p_i^2}{2m} + V(r_i)$$
then the solution to this equation $H\Psi = E \Psi$ ...

I am trying to derive the result for a kinetic hamiltonian in second quantization in term of the fields, that is: $\hat{H} = \int - \Psi^\dagger (r) \frac{\hbar^2\hat{\nabla}^2}{2m} \Psi(r)$
I start ...

Second quantization is sometimes considered to be a bad name, because a single quantization is enough. For electrons, we can either start from a many body viewpoint and introduce field operators or we ...

From the answer to this question Computing $\langle0|T[Q(t_2)Q(t_1)]|0\rangle$, I have discovered that there is two perspectives to QFT. I am doing a course which is unfortunately a summary of QFT and ...

My Question
Are the operators for the $A$, $E$ and $B$ field to be treated as operators in a Heisenberg description or is their time dependence explicit when performing a textbook EM quantization as ...

In the above extract from Simons and Altman: Condensed Matter Field Theory, I am having trouble getting from (2.3) to (2.4) in the case of Fermions (ζ=-1 and the n(subscript i) values are modulo 2).
...

Does any one know if it is possible to find the relation between the ac current frequency applied to a piezoelectric and the change in the crystal lattice due to this current BY USE OF HAMILTONIAN (in ...

I often see a Hamiltonian in second quantization written for the valence and conduction band. Now, I was wondering: What are the single-electron states that form the prouct state they act on? So what ...

I found two notions of states for second quantization.
One representation uses occupation numbers here, for example
Another one creates the n+1 th particle in a collection of n existent states. see ...

I am trying to quantize the quartic potential $(\lambda/4!)\phi^{4}$ in a box of side length $L$, with periodic boundary conditions. I have expanded the field
$$\phi = \sum \limits_{\vec{n}} \exp(i ...

In hopping model, we can get the Hamitonian as $H_0=-t\sum a^\dagger_ia_{i'}$. Then we take the fourier transform and put the operator which are in momentum space in the Hamitonian above. However, I ...